Two Pulleys with two acceleration and two tensions (Diagram included)

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Wara
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pulley

Homework Statement


Two masses are attached together by means of light inextensible strings and light frictionless pulleys as shown in the diagram. The system is released and the upper block slides along the table. The coefficient of friction between this block and the table is 0.32. Calculate the magnitude of the tensions (T1 and T2) and accelerations while the blocks are acceleration.
http://content.screencast.com/users/Waraa/folders/Snagit/media/bc6a12fc-dd79-4db6-91a4-1057f75aca6e/03.10.2012-15.11.45.png

Homework Equations


(1) m1a1 = T1 - μmg
(2) m2aa = m2g - T2
(3) 2T1 = T2
(4) 2a2 = a1

The Attempt at a Solution


T1 = 113.7N
T2 = 196N

(1) + (2) + (3) + (4)
m1a1 + m2aa + 2T1 + 2a2 = T1 - μmg + m2g - T2 + T2 + a1
2a2 = T1 - μmg + m2g + a1

I'm stuck right there. Am I even doing it right?
 
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Wara said:

Homework Statement


Two masses are attached together by means of light inextensible strings and light frictionless pulleys as shown in the diagram. The system is released and the upper block slides along the table. The coefficient of friction between this block and the table is 0.32. Calculate the magnitude of the tensions (T1 and T2) and accelerations while the blocks are acceleration.
http://content.screencast.com/users/Waraa/folders/Snagit/media/bc6a12fc-dd79-4db6-91a4-1057f75aca6e/03.10.2012-15.11.45.png


Homework Equations


(1) m1a1 = T1 - μmg
(2) m2aa = m2g - T2
(3) 2T1 = T2
(4) 2a2 = a1


The Attempt at a Solution


T1 = 113.7N
T2 = 196N

(1) + (2) + (3) + (4)
m1a1 + m2aa + 2T1 + 2a2 = T1 - μmg + m2g - T2 + T2 + a1
2a2 = T1 - μmg + m2g + a1

I'm stuck right there. Am I even doing it right?
Hi Wara! :wink:
Wara said:
(1) m1a1 = T1 - μmg
(2) m2aa = m2g - T2
(3) 2T1 = T2
(4) 2a2 = a1

Fine so far! :smile:

ok, now you should substitute for a2 and T2 from (3) and (4) into (2):

(1) m1a1 = T1 - μmg
(2) m2a1/2 = m2g - 2T1​

then eliminate T1 :wink:
 
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tiny-tim said:
Hi Wara! :wink:


Fine so far! :smile:

ok, now you should substitute for a2 and T2 from (3) and (4) into (2):

(1) m1a1 = T1 - μmg
(2) m2a1/2 = m2g - 2T1​

then eliminate T1 :wink:

Thank you so much.